Question: 4 people can paint 3 walls in 48 minutes. How many minutes will it take for 7 people to paint 6 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 3\text{ walls}\\ p &= 4\text{ people}\\ t &= 48\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{3}{48 \cdot 4} = \dfrac{1}{64}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 6 walls with 7 people. $t = \dfrac{w}{r \cdot p} = \dfrac{6}{\dfrac{1}{64} \cdot 7} = \dfrac{6}{\dfrac{7}{64}} = \dfrac{384}{7}\text{ minutes}$ $= 54 \dfrac{6}{7}\text{ minutes}$ Round to the nearest minute: $t = 55\text{ minutes}$